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A method for simulating transient temperature field equation numerical values

A technology of transient temperature field and temperature field, applied in electrical digital data processing, special data processing applications, instruments, etc., can solve problems such as low efficiency and large amount of calculation of simulated temperature field, so as to improve calculation speed and solve problems efficiently and quickly Effects of the Transient Temperature Field Problem

Active Publication Date: 2019-06-14
BEIJING INSTITUTE OF PETROCHEMICAL TECHNOLOGY
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Problems solved by technology

[0004] In order to overcome at least to a certain extent the problems of large amount of calculation and low efficiency in simulating the temperature field in the related art, an embodiment of the present invention provides a method for simulating the numerical value of the transient temperature field equation, specifically as follows:

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  • A method for simulating transient temperature field equation numerical values
  • A method for simulating transient temperature field equation numerical values
  • A method for simulating transient temperature field equation numerical values

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Embodiment 1

[0062] The invention provides a method for simulating the numerical value of the transient temperature field equation, see figure 1 , the method includes the following steps:

[0063] 101: Give the mathematical expression, boundary conditions and initial conditions of the transient temperature field equation;

[0064] 102: Multiply the imaginary temperature field on both sides of the transient temperature field equation, and integrate by parts to obtain the variational form of the original transient temperature field equation;

[0065] 103: Decompose the required temperature field u into a form that includes the sum of time and space function products;

[0066] 104: Substituting the separated form solution in step 103 into the variational scheme obtained in step 102, fixing the time domain, and deriving the equation about X in the space domain;

[0067] 105: Substituting the separated form solution in step 103 into the variational scheme obtained in step 102, fixing the spac...

Embodiment 2

[0073] As an improvement of the first embodiment, the embodiment of the present invention provides another method for simulating the numerical value of the transient temperature field equation, including the following steps:

[0074] Step 1: Write out the mathematical expressions, boundary conditions and initial conditions of the transient temperature field equation.

[0075] First, in the space-time domain Ω=Ω xy ×Ω t Above, the expression of the transient temperature field equation in two-dimensional space is:

[0076]

[0077] Among them, k is the thermal conductivity of rock or other media, a constant; f is the source term of the temperature field, a constant; t is a time variable; x, y are space variables, that is, the abscissa and ordinate; u is the temperature to be solved, which is The ternary function of space variable x, y and time variable t, namely u=u(x, y, t); Ω xy is the space area; Ω t for the time zone.

[0078] Secondly, the boundary conditions and in...

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Abstract

The embodiment of the invention discloses a method for simulating a transient temperature field equation numerical value, and belongs to the petroleum and natural gas engineering temperature field numerical simulation technology, and solves the problems of large simulated temperature field calculation amount and low efficiency in the prior art. The method comprises the following steps of multiplying virtual temperature fields on two sides of a transient temperature field equation, and carrying out partial integration to obtain a variational form of the original transient temperature field equation; decomposing the solved temperature field u into a form containing time and space function product summation; substituting the separation form into a variational format, fixing a time domain, deducing an equation about X in a space domain, fixing the space domain, and deducing an equation about T in the time domain; solving the equation about X and the equation about T through an alternatingdirection iteration method, repeating the process to obtain the value of each Xm and the value of each Tm, multiplying and accumulating the Xm and the Tm, and outputting a temperature field u. The method is mainly used for simulating the numerical value of the transient temperature field equation.

Description

technical field [0001] The invention belongs to the technical field of numerical simulation of oil and natural gas engineering temperature field, and in particular relates to a PGD (Proper Generalized Decomposition) numerical method for simulating a transient temperature field efficiently and quickly. Background technique [0002] The change of temperature field is accompanied by the process of drilling, oil production and transportation in the field of petroleum engineering. Therefore, it is of great theoretical and practical significance to study the numerical calculation method of temperature field. Accurate prediction of temperature field change in oil production will help to improve the final Oil and gas recovery. [0003] At present, the methods for simulating the temperature field equation include finite difference method, finite volume method, and finite element method. These numerical methods uniformly process the temperature field in the time domain and space domai...

Claims

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Application Information

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IPC IPC(8): G06F17/50
CPCY02E60/00
Inventor 汪道兵塞尔吉奥·兹洛特尼克秦浩宇波孙东亮
Owner BEIJING INSTITUTE OF PETROCHEMICAL TECHNOLOGY
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